
where \(\bar{d}\)  is displacement operator in phase space, \(T\)  is amplification or attenuation and rotation operator in phase space, and \(\)  is a noise term that may consist of quantum as well as classical noise.
The thermal noise channel, which belongs to incoherent channel [1]}, of CV Gaussian quantum system can be written as [2]}
\(\begin{aligned}T&=\sqrt{\eta }~\mathbf {I},\\&=\left(1-\eta \right)\left( \delta +\upsilon \right)~\mathbf {I},\\\bar{d}&=0,\end{aligned}\) 
